Volume 159 No, February 017 Image based Cats ad Possums Idetificatio for Itelliget Trappig Systems T. A. S. Achala Perera School of Egieerig Aucklad Uiversity of Techology New Zealad Joh Collis School of Egieerig Aucklad Uiversity of Techology New Zealad ABSTRACT Eigeface based recogitio is widely used to idetify idividual faces. This techique is commoly used i huma recogitio domai. I this research, we are ivestigatig for implemetatio of a possible solutio; which ca be used to idetify species. The eigeface techique is a ovel approach i aimal recogitio domai [1, ]. I this applicatio, cats ad possums are targeted as species of iterest. The mai reaso for targetig cats ad possum is, these itroduced species are classified as threat to New Zealad atural eviromet ad ative wildlife. The ext phase of this research project is to implemet a visio based trappig system. This paper explais a ovel classifier to use with eigeface techiques to separate differet species. Keywords Euclidea distace, face recogitio, aimal detectio 1. INTRODUCTION It was foud, if the aimal images were used without ay paddig with the eigeface techique, the recogitio rate is extremely poor 55% for possums ad 33% for cats. This is mostly due to the face orietatio ad backgroud iformatio. These paper discuses, about improvemet of curret techique by backgroud removal, species groupig, backgroud colour optimizatio ad image scalig. The oe of the mai cotributio i this paper is, developmet of a ew method for separatio of eigeface outputs (Distace from mea). This ovel techique offers a ew tool, to trasform multi dimesioally scattered data clusters ito two dimesioal graph. Which allow users to see the separatio of differet class clusters, ad defie the decisio boudary. Fially, we explai the itroductio of error weight vector ad extra eigevalue to improve the separatio of two class problem.. EIGENFACE TECHNIQUE The eigeface techique is ormally used i huma face recogitio. I a typical applicatio, a traiig set is created with differet huma faces that eed to be idetified by the system. Firstly, calculates the mea of the traiig images, ad the mea is subtracted from the traiig set to obtai a mea-shifted traiig set. This is kow as ormalizig the traiig set. From the mea-shifted traiig set, the scrambled covariace matrix is calculated. The the eigevectors ad eigevalues are obtaied from scrambled covariace matrix. The eigevectors with largest eigevalues are kept for detectio. These are kow as the priciple compoets. These priciple compoets keep most of the facial features. Fially, the eigeface techique projects the mea-shifted images ito the eigespace, usig the pricipal eigevectors [1, 3-5]. The eigeface algorithm ca be explaied i few steps [1, 3, 5, 6]. Step 1: Obtai a aimal face traiig set I1, I,..., IM Step : Covert each image Ii ito a vector Γi (Covert the NxN image ito a Nx1 vector) Step 3: Calculate the average aimal face vector Ψ: Ψ = 1 M M i=1 Γ i Step 4: Subtract the average face from Γi to get Φi: Φi = Γi - Ψ () Step 5: Calculate the covariace matrix C: C = 1 M M =1 Φ Φ T = AA T N N Where A = Φ 1 Φ Φ M N M Matrix Step 6: Calculate the eigevectors ui of AA T [5] These are same as M best eigevectors from the largest eigevalues. Oce best eigevector from traiig set is computed, ukow images ca be feed through the system for face detectio. Before the detectio process, the iput image eed to be ormalized. This processed ca be split ito four steps for a give ukow image Γ [1, 3, 4]. Step 1: Calculate Φ = Γ - Ψ Step : Calculate Φ = K i=1 w i u i (w i = u T i Φ) Step 3: Calculate Euclidea distace e d = Φ Φ [5] Step 4: If e d < T d the Γ is a face I typical applicatio, Euclidea distace is calculated. The this distace is compared agaist a kow threshold value. If the Euclidea value is less tha the threshold, the iput ukow image is oe of the traiig set images. Otherwise it is ot 3. EIGENFACE TECHNIQUE WITH DEVELOPED DISTANCE CLASSIFIER The eigeface techique with developed distace algorithm ca be described as follow. The size of the traiig image I (1) (3) (4) 1
Volume 159 No, February 017 is m 1 matrix. I a traiig set (A) there are (N) umber of images (refer to equatio (5)). The average face μ is calculated refer to equatio (6).The ormalize the traiig set by subtractig the average face as show o equatio (7). The scramble covariace matrix B is calculated from ormalized images (refer to equatio (8)) A = I 1, I, I 3,, I N (5) (6) μ = NI B = A μ (M N matrix) (7) B T B (8) Cov B = N 1 M N matrix Use B T B isted of BB T The eigevalue λ ad eigevectors e are calculated. Where: 4. IMPROVING DETECTION RATE BY OPTIMISING THE IMAGE COLOUR SCHEME Oe of the developed techique is optimizig the image color scheme. Durig the iitial ivestigatios few color schemas were trials. The iitial color scheme was; the image backgroud color as grey (itesity value of 131). The iteral face color was white (itesity value 55) ad preserves the ose ad eyes iformatio as origial colours (refer to Figure 1). The mai issue of this scheme was, the area of ose ad eyes was smaller percetage compare to the rest of the area of the image. The differet betwee grey ad white is sigificat eough to produce strog eigevectors to extract the face outlie iformatio. Therefore, the separatio of the species classes is ot sigificat eough. B T Be = λ e (9) The: BB T Be = Bλ e = λ Be (10) Therefore, ormalized eigefaces equal: f = Be Be is eigevectors of BB T ad λ is eigevalues Hece for full covariace matrix B: Eigevectors are f Eigevalues are λ = σ N 1 where σ is variace The for ukow image J, weights ad distace ca be calculated by usig equatio (13). w = J μ f (1) w w (13) distace = = (N 1) σ λ The developed distace formula (13) measures the distace to each image from the mea. This algorithm compesates for the effect of the larger weights by dividig them by its eigevalues (effectively the variace). Sigificat eigevectors have the larger eigevalues. Sigificat eigevectors also produce sigificat weights. For a example if we have 5 images as a data base the covariace matrix size is 5x5. Oce it covert to eigevector ad value, it ca be observed sigificat eigevectors have larger eigevalues. Similarly, mai eigevectors produce larger weights. The fist vector of the eigevector matrix is ot meaigful due the ormalizatio of the traiig images. This also illustrates i eigevalue matrix; the first eigevalue s magitude is isigificat compare to other eigevalues. Previous ivestigators foud that, three eigevectors with largest eigevalue mostly cotai the iformatio about backgroud lightig [6]. Accordig to [6] research project, by removig three eigevectors with largest eigevalues, improves the accuracy of the classifier. But this developed distace algorithm (13), reduces the effect of the sigificat eigevectors, by dividig the sigificat weights with its eigevalue. Figure 1: First trialed color scheme (11) The secod scheme was, backgroud colour as black (itesity value of 0), face color as grey (itesity value of 160) ad eyes ad ose color as white (itesity value of 55) (refer to Figure (a)). The mai idea behid this scheme was to produce a large itesity chage betwee backgroud ad face. Similarly eyes ad ose bee white (55) they have larger represetatio of the image ad aother sigificat itesity step chage betwee face ad features. This schemes produces much better separatio betwee facial outlie ad backgroud, compare to first scheme. Eve though eyes ad ose have much higher itesity value compare to face still a small area. Sice eyes ad ose are smaller regios, it was decided to aalyze the species separatio without eyes ad ose. I the third scheme trial image was simplified further by chagig the face color to white (itesity value of 55) ad backgroud color to black (itesity value of 0) (refer to Figure (b)). It was foud this cofiguratio produces best result due to maximum step chage betwee backgroud ad face shape. I this scheme, the recogitio was targetig o face outlie. The outlie had the mai itesity step chage. 13
Volume 159 No, February 017 (a) Figure : (a) Secod colour scheme (b)third trailed colour scheme 5. IMPROVING DETECTION RATE BY OPTIMISING IMAGE RESOLUTION The image size is oe of the importat parameters, which ca be used to optimized the separatio of the species classes. Image size directly proportioal to the size of the full covariace matrix. Therefore, Eige face techique uses scrambled covariace matrix to reduce the umber of data poit. The mai issue of takig the scrambled covariace matrix (B T B istead of BB T ), large amout of the useful data will be lost. For a example, if there is a traiig set of 0 images ad each image is 170 x 170 pixels. The actual size of the covariace matrix BB T will be a matrix of 8900 x 8900. Sice this matrix is computatioally demadig, therefore scrambled covariace matrix B T B is used. Scrambled covariace matrix is 0 x 0. Eve though the most useful eigevectors are kept, the large portio of data is lost. I order to improve this situatio, oe of the techique we developed was reduce the image resolutio. Sice we are tryig to detect aimal by facial shape, fur details ad ose ad eyes iformatio are ot vital. Therefore, image size ca be reduced to miimize the data lost due to the scrambled covariace matrix. For a example if we cosider same traiig set of 0 images, but this time all the images are 10 x 10 resolutio. The full covariace matrix BB T will 100 x 100. If scrambled covariace matrix is use, it size will be still the same size 0 x 0. But the overall data lost lot more data tha, first example. I order to fid the optimal image resolutio, three differet image resolutio were ivestigated. The image resolutios were 34 x 34, 17 x 17 ad 10 x 10. To reduce the resolutio, image was divide ito differet size blocks. For a example to obtai 17 x 17 image, origial image (resolutio 170 x170) was divide ito 17 x 17 blocks. Each block is 10 x 10 pixels. The take the sum of all the pixel i each block. Each sum was divided by its pixel cout ad replace the whole block with the calculated value (block average). Usig this techique all the pixels iformatio is still kept (refer to Figure 3). (b) Figure 3: Image resolutio from left to right 170 x 170, 34 x 34, 17 x 17 ad 10 x 10 After this process, all the images have black backgroud but facial edge cotour colour was chaged to differet shade of grey values (refer to Figure 4). It was foud 17 x17 is the optimum resolutio, with best separatio betwee cat ad possum classes. Figure 4: 34 x34 image with grey facial cotour 6. SPECIES CLASS SEPARATION WITH DEVELOPED DISTANCE CLASSIFIER Usig equatio (13) distace betwee mea image ad give image ca be calculated. I possums ad cat detectio problem, there will be two differet distaces for ay give image. I order to develop a classifier to discover which cluster is close to the give image. Or i aother word which side of the decisio boudary the ukow image lies. Trivial method of implemetig above is, by compariso of these two distaces. Shortest distace to the class mea could be selected as the likely species for a give image. Sice this is multidimesioal problem, it is hard to defie the decisio boudary betwee these two aimal classes i multidimesioal space. Therefore, it is importat to implemet a ovel techique which covert distace data from multidimesioal space to two dimesioal (D) space. I D space decisio boudary ca be defied to classify a give ukow image. I order to trasform multidimesioal space data poit ito D space, trigoometrical space is used. Sice there are two distaces (cat distace ad possum distace) i multidimesioal space, these two distaces ca be plotted i trigoometrical space. It ca be assumig i trigoometrical space, cat mea image ad possum mea image is separated by a certai fixed distace. This distace ca be set as a legth betwee shorts distaces vectors (cat distace ad possum distaces). The the ukow image distaces ca be ca be plotted from fixed mea poits. The agel of both 14
Volume 159 No, February 017 distace vectors ca be calculated accordig to the poit, where those two vectors meet i trigoometrical space (refer to Figure 5 (a)). I order to plot these poit, there are three scearios, which eed to be take ito cosideratio. First case distace form cat traiig set ad possum traiig set has similar weight vectors. So all the poits will scatter betwee cat ad possum mea values (refer to Figure 5 (b)). I case two, oe of the distace get cosiderably larger tha other. Therefore, the poit will pass oe of the mea values (refer to Figure 5 (c)). I third case oe distace is extremely lager tha the other, hece those two magitudes will ot be able to yield a poit. The first two cases ca be calculated usig the developed algorithm below. (a) (b) Dc Dc Dp Dc = Cat Distace Dp = Possum Distace µ c µ p a Dc + Dp = Miimum Distace h L µ c µ p b Dp θ a = L + ll + l + () a = L + ll + b (3) l = a L b L (4) = b l (5) Equatios (18), (19), (4) ad (5) ca be used calculate the poit o the graph. If ay poit belogs to the case three, the it will ot be able to plot o the graph. Figure 9 shows the example classes separatio of developed classifier. Oce classes are separated as show o Figure 9, the decisio boudary ca be defied. 7. IMPROVING DETECTION RATE BY INTRODUCING ERROR WEIGHT VECTOR I this ovel techique, ew weight vector is itroduced to compesate for omitted iformatio by selectig scrambled covariace matrix B T B. Firstly, cats ad possums are separated ito two differet traiig sets. The eigeface techique is applied to both traiig sets. This time ormalized eigefaces are f = Be Be used. At the ed of the process, we eded up with two differet traiig weights oe for possums ad cats C P w ad w. Oce this process is completed additioal weight vector ca be calculated as show below. Where: eigefaces = f image = i m a (c) L µ c µ p Figure 5: (a) Image distaces o trigoometrical space (a) Case oe (b) Case two Case 1: From low of cosie a ca be expressed as [7]: a = b + L bl cos θ (14) cos θ = b + L a bl (15) L = l 1 + l (16) l 1 = b cos θ (17) l 1 = b + L a L = a l = b l 1 Case : ad l = a + L b L From Pythagorea theorem a ca be expressed as [8]: a = + L + l (0) b = + l (1) b h (18) (19) For each image w weight vector ca be calculated: w = i m f (6) i m = Ideally: i m f = w k f k k w k f k f k f k f = 1 if k = ad f k f = 0 if k (7) (8) i m f = w (9) I practice e m error vector ca be calculated as below error e m = i m w k f k k The e m ca be used as a extra weight vector. The above algorithm basically, calculate the weight vectors for the traiig images usig modified eigeface techique. After that for a give image i m weights ca be calculated usig the eigeface. The these calculated ew weight are used to recostruct the origial image i m. Fially, recostructed image is subtracted from actual image to fid the differece betwee these two images. The resultig differece is used as a extra error weight vector e m. This ca be icluded ito the existig weights. Oce error weight is calculated from the image, 15
Volume 159 No, February 017 correspodig magitude (eigevalue) is required for the Iside the ukow images, first images were possums ad vector. I order to fid the ext eigevalue, existig remaiig 18 were cats (refer to Figure 7 (b)). These traiig eigevalue ca be used. If we plot the eigevalue, it has a expoetial decay (refer to Figure 6) [9]. The expoetial decay formula (31) ca be used to fid the ext eigevalue. sets ad test images were scaled as discussed i sectio 5. All the traiig images ad test images are 17x17 resolutio. I this roud of experimets error weights (refer to equatio (30)) are ot used. N t = N 0 e λt (31) Where t ad λ are kow as the decay costat, ad e x is the expoetial fuctio ad N 0 = N zero is the iitial value [10]. The decay costat ca be expressed as equatio (3). The proof ca be foud i [10, 11]. l N N 0 = λt (3) 17x17 Images Eigevalues (a) 10000000 5000000 0 1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 31 Eige Values Possums Eige Values Cats Figure 6: Graph of eigevalue Vs magitude The above algorithms (equatios (31) ad (3)) ca be used to calculate the extra error weights ad eigevalues for possums ad cats w ad w C P classes. By addig the error weight ad estimated eigevalue, the classes separatio ca be icreased ad data poits withi the class clustered together tighter. 8. CLASSIFIER EVALUATION The mai aim of this sectio is to evaluate the developed ew distace algorithm (refer to equatio (13)) with existig eigeface distace algorithm d = w. I this study, four differet combiatios were aalysed. Firstly, existig eigeface techique (33), secodly improved eigeface techique (34), thirdly existig eigefaces with developed distace algorithm (35), fially improved eigefaces with existig distace formula (36). Optio oe: Stadard Optio two: Proposed f = Be f = Be Be d = d = w w N 1 λ (33) (34) (b) Figure 7: (a) Traiig images (b) Ukow test images To plot the data developed plottig techique was used. This developed classifier helps to aalyse the separatio betwee species classes. If the classes are closer together, it is hard to defie a decisio boudary. The four figures below idicate the performace of all four optios (refer to Figure 8, Figure 9, Figure 10 ad Figure 11). Optio three: Optio four: f = Be d = w f = Be Be d = w N 1 λ (35) (36) Figure 8: Graph for optio oe Where f is eigefaces, B is mea subtracted (ormalised) images, e is eigevectors, w is weights ad d is distace. I order to test these algorithms, two traiig sets with 33 images i each traiig set were selected (refer to Figure 7 (a)). The 40 ukow images were used, to tests the system. 16
Volume 159 No, February 017 together, we ca archive the maximum separatio betwee classes. Stadard eigeface techique has the worst performace out of all four optios. It shows ill separatio betwee two aimal spices. Some what this is expectable result due to vectors with arbitrary magitudes i face-space (low-dimesioal space). Perhaps this could be oe of the reasos; the origial eigeface techique used threshold based detectio techique. The itroduced error weight vector ad eigevalue, helps to tight up the species clusters closer together. Also improves the separatio of the two clusters. The Figure 1 demostrates the improved separatio betwee two classes. Figure 1 ad Figure 9 were plotted with same traiig ad test data set. The differece is Figure 1 was plotted with itroduced error vectors but Figure 9 was ot. Figure 9: Graph for optio two Figure 10: Graph for optio three Figure 11: Graph for optio four If we aalyse these four graphs; it ca be clearly see the best separatio is achieved by improved eigeface techique (refer to equatio (34)). The secod best optios are optio 3 ad 4. Eve though, these two techiques have differet scales o X ad Y axis, both graph have exactly the same separatio. So it ca be cocluded the effect o the weights, is similar, either for ormalised eigeface or dividig the ormalized weights by their eigevalue. Whe we combie these two factors Figure 1: Graph for optio two with itroduced error weights ad eigevalue 9. CONCLUSION AND FUTURE WORKS This developed ovel techiques, improve the detectio rate of the typical eigeface techique. The optimized algorithm ca be used to solve ay two class problem. I this applicatio it was used to detect cats ad possums. The developed data visualisig techique trasform multidimesioal data, ito two dimesioal plot. Which allows user to idetify the targeted clusters ad defie the decisio boudary aroud the clusters. The data cluster separatio is optimized by alterig the image color schema ad scale. By itroducig error weights, made the data clusters tighter ad the same time icrease the separatio. The ext phase of the project is to implemet the developed algorithm i Raspberry PI embedded module. The mai advatage of the eigeface techique is, it allows most of the processor itesive portio of the algorithm to compute i a powerful desktop computer ad store the calculated weights ad eigeface iformatio i the embedded module. The oly processig task left is, to detect the ukow aimal image from the Raspberry PI camera module. 17
Volume 159 No, February 017 10. REFERENCES [1] T. A. S. A. Perera ad J. Collis, "A Novel Eigeface based Species Recogitio System," Iteratioal Joural of Computer Applicatios, vol. 115, pp. 19-3, April 015. [] T. A. S. A. Perera ad J. Collis, "Imaged Based Species Recogitio System," i 015 9th Iteratioal Coferece o Sesig Techology (ICST), Aucklad 015, pp. 195-199. [3] M. A. Turk ad A. P. Petlad, "Face recogitio usig eigefaces," i Computer Visio ad Patter Recogitio, 1991. Proceedigs CVPR '91., IEEE Computer Society Coferece o, 1991, pp. 586-591. [4] M. Smiatacz, "Eigefaces, Fisherfaces, Laplaciafaces, Margifaces How to Face the Face Verificatio Task," i Proceedigs of the 8th Iteratioal Coferece o Computer Recogitio Systems CORES 013. vol. 6, R. Burduk, K. Jackowski, M. Kurzyski, M. Woziak, ad A. Zolierek, Eds., ed: Spriger Iteratioal Publishig, 013, pp. 187-196. [5] M. Turk ad A. Petlad, "Eigefaces for Recogitio," Cogitive Neurosciece, Joural of, vol. 3, pp. 71-86, 1991. [6] P. N. Belhumeur, J. P. Hespaha, ad D. Kriegma, "Eigefaces vs. Fisherfaces: recogitio usig class specific liear projectio," Patter Aalysis ad Machie Itelligece, IEEE Trasactios o, vol. 19, pp. 711-70, 1997. [7] M. Abramowitz ad I. A. Stegu, Hadbook of Mathematical Fuctios with Formulas, Graphs, ad Mathematical Tables, 9th ed. New York: Dover, 197. [8] W. W. R. Ball ad H. S. M. Coxeter, Mathematical Recreatios ad Essays. New York: Dover, 1987. [9] S. Alakkari ad J. J. Collis, "Eigefaces for Face Detectio: A Novel Study," i Machie Learig ad Applicatios (ICMLA), 013 1th Iteratioal Coferece o, 013, pp. 309-314. [10] E. W. Weisstei. "Expoetial Decay." From MathWorld--A Wolfram Web Resource. Available: http://mathworld.wolfram.com/expoetialdecay.html [11] J. Stewart, Calculus Cocepts Ad Cotexts Gary W. Ostedt, 001. IJCA TM : www.ijcaolie.org 18